Enzymes Quinate Dehydrogenase (E.C.1.1.1.24) and 5

THE ABSOLUTTE STEREOCHEMICAL COUtRSE OF CITRIC ACID BIOSYNTHESIS* BY KENNETH R. HANSON AND IRWIN A. RoSEt

DEPARTMENTS OF BIOCHEMISTRY OF THE CONNECTICUT AGRICULTURAL EXPERIMENT STATION AND OF YALE UNIVERSITY SCHOOL OF MEDICINE, NEW HAVEN Communicated by H. B. Vickery, September 3, 1963 In 1948 Ogston noted that when such symmetrical molecules as citric (or amino- malonic) acid are acted upon by asymmetric enzyme surfaces, pairs of identical groups may well be differentiated.1 Shortly thereafter it was shown, by using labeled substrates, that the two -CH2COOH groups of citric acid could, in fact, be distinguished.2 When citrate is formed from oxaloacetate and acetyl-CoA by citrate synthase (E.C.4.1.3.7, condensing enzyme), and is then treated with aconitate hydratase (E.C.4.2.1.3, aconitase) to form cis-aconitate and threo-Dr-isocitrate, the -CH2COOH ends of these compounds are derived from acetyl-CoA, while the other atoms are derived either from oxaloacetate or water.3-6 The acetyl-CoA-derived group yields acetate when citrate is cleaved by citrate-lyase (E.C.4.1.3.6, citratase),7'8 and acetyl-CoA when citrate is attacked by the citrate cleavage enzyme.9 The nonequivalence of the two -CH2COOH groups is apparent when citric acid is represented as I (heavy line above, dotted lines below the plane of the paper). Carbon atoms 1 and 2 are to 5 and 4 as right arm is to left arm:'0 they cannot be superimposed except by reflection. The same molecule is shown in Emil Fischer projection as II (vertical lines below and horizontal lines above the plane of the paper). The carbon atoms are numbered according to the Hirschmann convention.11 The major purpose of the present investigation has been to determine which -CH2COOH group, in the absolute stereochemical sense of I, is derived from acetate and which is derived from oxaloacetate. In order to differentiate the two groups it was necessary to obtain asymmetrically labeled citric acid from a labeled compound of known absolute configuration. The following procedure is based upon the investigations, by Dangschat and H. 0. L. Fischer, of the stereochemistry of quinic acid,'2 and by Davis and his associates of the biosynthesis of this compound.'3 In the first stage quinic acid labeled with tritium in the 6 position was obtained with the aid of an extract of Aerobacter aerogenes A170-143 known to contain the enzymes quinate dehydrogenase (E.C.1.1.1.24) and 5-dehydroquinate dehydratase (E.C.4.2.1.10).'3 Thus 5-dehydroshikimic acid (III) yielded 5-dehydroquinic acid- 6-T (IV), which on reduction gave quinic acid-6-T (V). The symbol,--, indicates that the configuration at the carbon atom bearing tritium is unknown. In the second stage V was oxidized to citric acid4-T (VII) by the method shown.'4 Lastly, the properties of (VII) as a substrate for aconitate hydratase were studied. Materials and Methods.-Enzyme preparations: Cells of A. aerogenes A170-143 were grown, with stirring at 370 for 24 hr, on minimal medium A15 supplemented with 20 mg of yeast extract (Difco) and 600 mg of quinic acid (volume 1 liter). Mucoid growth was not observed. The post log phase cells were washed with water, suspended in 0.033 M Tris-HC116 buffer, pH 7.5, and sonically disrupted. The initial extract (42 mg of protein from 1 ml of packed cells) showed strong NADH oxidase activity. After treatment with MnCl21' and dialysis against 0.033 M 981 Downloaded by guest on September 30, 2021 982 BIOCHEMISTRY: HANSON AND ROSE PROC. N. A. S.

5 4 OH 2 COOH 5 Tris-HCl buffer, pH 7.5, this activity was HOOC H2C T ,CH2COOH (A) H-C-H (P) 4 found to be negligible. The preparation vs,, (26 mg of protein) contained both quinate 'HUVU-C-OH dehydrogenase and 5-dehydroquinate de- COOH (P) H - -H tA) 2 hydratase. The specific activity of the COOH former was 1.06 units/mg of protein at pH 9.4.13 A small amount of 5-dehydroshikimic acid brought about the rapid oxidation FIG. 1. of NADH (pH 7.4, 0.72 units/mg of protein). No appreciable losses of these activities occurred on storing the frozen solution at - 100 or on lyophylization. The A. aerogenes mutant was a gift of Dr. Bernard Davis. Aconitate hydratase was prepared from pig heart and stored as a frozen solution.'7 Before use it was activated with Fe2+ and cysteine. Isocitrate dehydrogenase (E.C.1.1.1.42) and glutamate dehydrogenase (E.C.1.4.1.3) in phosphate buffer were purchased from Boehringer. Throughout this paper a unit of enzyme is defined as that amount which catalyzes the trans- formation of 1 pmole of substrate/min at room temperature under optimum or specified conditions. Quinic acid-6-T: (a) From 5-dehydroshikimic acid: To the lyophylized enzymes (0.43 mg protein), buffer pH 7.4 (Tris-HCl, 100 stmoles in 33 ,1), 5-dehydroshikimic acid (8 jsmoles), tritiated water (0.25 ml), and, finally, NADH (13 ,umoles) were added and the reaction mixture left at 240. The oxidation of NADH was followed by diluting 5 jul aliquots to 1 ml with 0.1 M NaOH (added to terminate the reaction) and observing the decrease in absorbancy at 340 mMA. The oxidation was complete in 35 min, at which time further reaction was prevented by adding HCl (100 Mmoles). The tritiated water was removed by vacuum sublimation. Water was added and then removed by distillation, and this operation was repeated until all the easily exchangeable tritium had been displaced. The specific activity of the water in the reaction mixture was 578,000 cpm/Muatom. The 5-dehydroshikimic acid was a gift of Dr. P. R. Srinivasan. (b) From quinic acid: The enzymes (0.43 mg of lyophylized protein) in tritiated water (0.3 ml) were added to a lyophylized mixture of Tris-HCl buffer pH 7.4 (100 Moles), NAD + (1 MAmole), and potassium quinate (10 jMmoles). The reaction mixture was maintained at 240 for 2 hr and 370 for a further 6 hr. Samples were withdrawn at various times, and the extent of incorporation was estimated. The specific activity of the water in the reaction mixture was 1 X 106 cpm/ uatom. The reaction was terminated as in experiment (a). Citric acid-4-T by oxidation of quinic acid-6-T: A sample containing less than 10 Mmoles of tritiated quinic acid was chromatographed on a Dowex 1 acetate column." Measurements of radioactivity served to locate the quinic acid peak. The combined peak fractions were concentrated to dryness, periodic acid (100 Mumoles, 0.1 ml) was added, and the solution left in the dark at 240 for 1 hr. Under these conditions quinic acid consumes exactly two molar proportions of periodate, the reaction being complete in about 10 min. Periodic and iodic acids were removed with the aid of a Dowex 1-X8 formate column (7 X 0.7 cm). The column was developed with 3 N formic acid and the first 16 ml of effluent were concentrated to dryness. Water (2 ml) and bromine (10 Ml) were added and the solution left in the dark at 27° overnight. The excess bromine was removed with a current of air and the reaction products were chromatographed on a Dowex-1 formate column.'8 The citric acid was located by radioactivity measurements. The over-all yield, based on radioactivity, was about 50%. The yield was not improved by adding strontium carbonate to the bromine oxidation mixture.'9 The specific activity of the citric acid from quinic acid was: method (a) 240,000 cpm/Mmole, and (b) 435,000 cpm/pmole.

COOH HOs COOH HN0M COOH HO% COOH HON0 COOH

nT x:) NbT4T/( T

\O..HNf-OHC CH HOOC COOH ' ~~0 0 111 IV V VI VII FIG. 2. Downloaded by guest on September 30, 2021 VOL. 50, 1963 BIOCHEMISTRY: HANSON AND ROSE 983

The oxidation process was studied in greater detail. A sample containing quinic acid (176,000 cpm) labeled by method (b) was diluted with potassium quinate (250 Mmoles), and the solution chromatographed as above. The amount of acid in the various dried fractions was determined by titration, and 93%/O of the applied radioactivity was associated with the quinic acid peak. An isotope effect was observed: the specific activity fell linearly by 26% from the front to the tail of the peak; mean 617 epm/,umole. The sodium quinate fractions were combined and the solution was passed through a short Dowex 50-H+ column to give the free acid which was then oxidized. When the final reaction mixture was chromatographed, a series of peaks were recorded. The fourth and last peak corresponded to citric acid (33% yield). The specific activity of the acid increased by about 10% from the front to the tail of the peak. The mean specific activity (620 cpm/umole) was in close agreement with that of the quinic acid. Tritiated citric acids for control experiments: From isocitrate+T20: threo-D.-isocitric acid (from crassulacean plants) was treated with aconitate hydratase in the presence of tritiated water and the enzyme destroyed by heating. The residual isocitrate was converted to a-ketoglutarate with isocitrate dehydrogenase, and the mixture of acids separated by silica gel chromatography.20' Tritium was not incorporated into cis-aconitic acid. The incorporation into citric acid was 60% of the equilibrium value assuming labeling at a single position.2 Specific activity: 85,000 cpm/ Jzmole. From isocitrate-3,4,4-T: A mixture of the four possible isocitric acids was prepared by the method of Fittig and Miller22 23 using tritiated succinic acid (New England Nuclear). The threo-D8L8 mixture was separated from the erythro-D8L. mixture [(±i)-alloisocitric acid] and from succinic acid by chromatography on a Dowex 1 formate column.'8 The threo-isocitric acids were eluted slightly ahead of the erythro mixture (ratio threo: erythro, 22:1). The threo mixture was treated with aconitate hydratase, and the citric acid formed was isolated by silica gel chromatography. Specific activity: 386,000 epm/umole. From isocitrate-2-T: A mixture of the four stereoisomers of isocitric acid in roughly equal proportions (from New England Nuclear; synthesized by the method of Wislicenus and Nas- sauer24) was treated with aconitate hydratase, and the citric acid formed was isolated by silica gel :and ion exchange chromatography. Specific activity: 50,000 cpm/,umole. In each of these preparations the treatment with aconitate hydratase was continued for at least six times the period required to establish equilibrium with untritiated isocitrate. Results.-Two methods were adopted for the preparation of quinic acid-6-T. In method (a) 5-dehydroshikimate was converted to quinate in the presence of tritiated water with NADH and the A. aerogenes enzyme preparation. The specific activity of the citric acid finally isolated was about half that of the tritiated water. If it is assumed that the oxidation of quinic to citric acid takes place with- out loss of tritium and that quinic acid can be labeled at only the one position, then a relatively small (twofold) discrimination against the tritium of the medium occurred. Discriminations as high as 40-fold have been observed.24 In order to establish that this was characteristic of the 5-dehydroquinate dehydratase reaction. it would be necessary to show that this enzyme was present in a rate-limiting amount in the reaction mixture. In method (b) the attempt was made to bring quinic acid into equilibrium with tritiated water through the enzyme-catalyzed cycle of oxidation, dehydration, hydration, reduction. Despite the long period of equilibration, the specific activity of the derived citric acid was only half that of the tritiated water employed. Although the oxidation of quinic to citric acid was not quantitative, the specific activities of the two acids were in close agreement. It follows that position 4 of quinic acid was not significantly tritiated. If nonenzymatic tritiation had taken place at the 5-dehydroquinate stage, labeling on both Ca4 and C-6 (adjacent to the keto group) would be expected. Comparison of citric acid-4-T with tritiated citric acids prepared by other methods: Downloaded by guest on September 30, 2021 984 BIOCHEMISTRY: HANSON AND ROSE PROC. N. A. S.

Investigations in a number of laboratories into the action of aconitate hydratase have shown that three types of isotopic labeling of the four methylene hydrogens of citric acid may be distinguished: (1) Of the two hydrogens on the oxaloacetate- derived methylene group of citrate, one remains attached to the carbon atom and appears on C-2 of cis-aconitate and threo-D4-isocitrate when citrate is acted upon by aconitate hydratase. When the isocitrate is oxidized by NADP +in the presence of isocitrate dehydrogenase to give a-ketoglutarate, this hydrogen is transferred to the 4P position (the A side)"' 26 of the coenzyme-reduced nicotinamide ring.6 27, 28 (2) The other hydrogen of this methylene group passes to water when the substrate is brought to isotopic equilibrium with aconitate hydratase. Conversely, hydrogen from the water passes to this position of citrate, but none is incorporated into cis-aconitate. In the interconversion of citrate and isocitrate, not all of the molecules pass through the free cis-aconitate stage. Hydrogen from the hydratase- exchangeable position of citrate may pass to the C-3 position of isocitrate, and vice versa.21' 29 The total replacement of hydrogen observed on isotopic equilibration is thus the result of repeated cycling of the substrates. (3) The hydrogens on the acetate-derived methylene group appear on C4 of a-ketoglutarate when citrate is acted upon by the coupled system aconitate hydratase and isocitrate dehydrogenase.5 The results of comparing samples of citric acid-4-T (tests), preyared from quinic acid-6-T, with tritiated citric acids labeled in the above three ways (controls) are shown in Table 1. Both test samples behaved almost precisely as the citric acid prepared from unlabeled threo-D8-isocitrate and tritiated water: nearly all of the tritium was released to the water on prolonged incubation with aconitate hydratase. The citric acids prepared from isocitrate-2-T or -3,4,4-T behaved otherwise: less than 10 per cent of the radioactivity was so released. When the residues from the equilibrium reaction were enzymatically converted to a-ketoglutarate and the a-ketoglutarate converted to glutamate, 79 and 86 per cent of the remaining radioactivity terminated in NADPH and glutamate, respectively. It follows that the maximum fraction of the test citric acids labeled in the acetate-derived methylene is 0.02 per cent and in the oxaloacetate-derived methylene, at the position not associated with the aconitate hydratase exchange reaction, is 2 per cent. A further test was performed on a sample of citric acid4-T (from 5-dehydroshikimic acid) with use of the coupled aconitate hydratase-isocitrate dehydrogenase system. The dehydrogenase was present in such a quantity that the rate of in- crease in absorbancy at 340 mAu was determined by the aconitate hydratase reaction. Throughout the reaction the ratio of tritium released to the water to NADPH formed was essentially constant. This result was typical of experiments performed on citric acid obtained by exchange labeling with tritiated water and aconitate hydratase. The same result has also been observed with various preparations of the hydratase. The fraction of tritium appearing on the C-3 position of a-ketoglutarate when test and control samples were acted upon by the coupled system varied from 40 to 17 per cent for reasons which are not at present understood. Discussion.-The above results may be summarized as follows: The tritium of citric acid4-T, obtained from enzymatically labeled quinic acid-6-T, is released to the water when the citric acid is acted upon by aconitate hydratase. Since the portion of the rmolecule derived from oxaloacetate is known to bear the hydrogen Downloaded by guest on September 30, 2021 VOL. 50, 1963 BIOCHEMISTRY: HANSON AND ROSE 985

TABLE 1 EQUILIBRATION OF TRITIATED CITRIC ACIDS WITH ACONITATE HYDRATASE Total radioactivity Distribution of Counts- (water + a% Into residue- %Into Tritiated citric acids residue), % Into Total Into glutamic cpm water NADPH acid Tests: citric acid-4-T derived from (a) 5-Dehydroshikimate 23,323 97 3 0 0.01 (b) Quinate 36,640 95 5 1.5 0.015 Controls: tritiated citric acids prepared from (1) Isocitrate + T20 24,439 95 5 0 0.65 (2) Isocitrate-2-T 37,043 5 95 75 0.30 (3) Isocitrate-3,4,4-T 8,849 8 92 0 79.0 Samples of quinic acid-6-T (V) were prepared from the compounds indicated (methods a and b) with the aid of 5-dehydroquinate dehydratase and quinate dehydrogenase, and these samples were oxidized to citric acid-4-T (VII). The three types of tritiated citric acids employed as controls were prepared from labeled or unlabeled isocitrate by prolonged incubation with aconitate hydratase. Samples 1 and 2 bear tritium at the oxaloacetate-derived end of the citric acid molecule. Most of the tritium on C-3 of isocitrate-3,4,4-T should have passed to the water, giving citric acid labeled at the end of the molecule not involved in the aconitate hydratase reaction. Each type of citric acid (0.08-0.25 ;&moles) together with buffer (triethanolamine-HCl, 0.1 M, pH 8.1) and aconitate hydratase (0.01 units) was maintained at 300 for 9 hr (final volume 1.0 ml). The water of each reaction mixture was separated by sublimation in vacuo and the dried residue freed of easily ex- changed tritium by adding water and performing a further sublimation. The residue from each incubation was treated with additional aconitate hydratase (0.01 units) and isocitrate dehydrogenase (0.1 mg) in the presence of NADP (0.3 pmoles) and in a final volume of 1.0 ml. The reduction of NADP was followed by measuring the change in absorbancy at 340 mys. When the reaction was complete, the radioactivity of a sample was counted, and another sample was filtered through a column of octanol-treated charcoal (1.5 X 0.6 cm) which was subsequently washed with excess water. Since the combined effluent and washes showed no absorbancy at 340 mp, all the NADPH had been adsorbed by the charcoal. The difference in radioactivity between this material and the residue is taken as the NADPH-associated radioactivity. The remainder of the charcoal-treated solution was incubated with glutamate dehydrogenase (1.5 units), NADH (0.2 pmoles), and ammonium acetate (150 pmoles) in order to convert the a-ketoglutarate into i-glutamate (final volume 3 ml). Additional glutamic acid (10 pmoles) was added and the entire reaction mixture was chromatographed on a Dowex 1 acetate column (elution with 0.5 N acetic acid). Quantita- tive recoveries of glutamic acid were obtained. The radioactivity in this material represents the tritium derived from the methylene group of citrate not involved in the aconitate hydratase reaction. The signif- icant fraction of the radioactivity which cannot be assigned to any of the C-H positions of citric acid in the control samples 2 and 3 is considered to represent contamination with the isomers of isocitric acid that are not substrates for aconitate hydratase. The preparations were shown to be free from the threo-Ds-isomer by assay with ieocitrate dehydrogenase. Thus, the radioactivity found in NADPH and glutamic acid was derived from the citric acid present. exchangeable by aconitate hydratase,6 the stereochemical course of citric acid biosynthesis is established in absolute terms. The assignment may be expressed in several alternative ways: (a) Carbon atoms 6, 3, 4, and 5 of citric acid are derived from oxaloacetate and 1 and 2 from acetyl-CoA (see formulas I and II). (b) If the axis of the center carbon atom and its attached -COOH group is equated with the axis of the body so that the -COOH group is at the feet, and if the -OH is behind the body, then the acetyl-CoA-derived -CH2COOH group is to the right front, and the oxaloacetate-derived -CH2COOH group to the left front. (c) In the formation of citrate from oxaloacetate, the side of the carbonyl group attacked by acetyl-CoA is opposite to the side attacked by NADH in the formation of L-malate.30 This conclusion is based on a direct correlation with D(+)-glyceraldehyde: The configuration of quinic acid relative to D-glyceraldehyde is firmly established (the evidence has been reviewed elsewhere31). Although the study involves enzymatic labeling of quinic acid, the position of labeling is known from the known chemistry of the enzymatic substrates. It follows that, in setting forth the se- quence of reactions involved in the correlation, no assumptions are required con- cerning the steric course of any reaction. The absolute configuration follows, since the configuration of D-glyceraldehyde is believed to be identical with that adopted in the Emil Fischer convention.32 Downloaded by guest on September 30, 2021 986 BIOCHEMISTRY: HANSON AND ROSE PROC. N. A. S. H\ COOH COOH COOH COOH Two indirect correlations, based C\C 9-C-H- C-D H-C-D H- C-D DO I-CO- on optical rotation data, have been HOCH \ H H-C-OHC-ICOOH COOH CH. reported. Unfortunately, the argu- VilI IX X Xi C00OH ments employed lead to opposite conclusions. Thus, in the one study, D0\ /COOH~o COOH COON COON the enantiomeric forms of oxaloci- C HO 0-C-H D-C-H D-C-H

C OD- C-OH tramalic acid lactone-3,3-D were as- / CIH HOOC -C-OH HOOC 0 COOH COOI CHI signed configurations on the basis of x~l x111 x1v xv COOH Hudson's lactone rule. Oxidation FIG. 3. of the free acids gave the corre- sponding deuterated citric acids.- In the other, a configuration was assigned to (-)-2-chloromethyl-2-hydroxysuccinic acid by means of Brewster's rules.33 It had previously been shown3 that asymmetrically labeled citric acid could be obtained from this compound with the aid of sodium cyanide-C'4. Both groups of investigators arrived at the assignment reached in the present paper. However, the latter group base their conclusion on a misreading of the experiments of Wilcox et al.3 Given the premise that Brewster's rules apply, their conclusion must be reversed. We are indebted to Dr. Hirschmann for drawing our attention to this error. The configuration at the oxaloacetate-derived methylene group of citric acid has been correlated with the fumarate hydratase (E.C.4.2.1.2, fumarase) reaction by Englard.6 The trans-nature of this reaction has been established by Gawron et al.33 and by Anet.34 The conclusion that the C-4 methylene group of citric acid is derived from oxaloacetate leads to the summary of Englard's experiments (Fig. 3). In terms of the anterior (A), posterior (P) convention of Hirschmann,'1 citric acid-4(A)-D (XI) arises from fumaric acid-2,3-D (VIII) by way of L-malic acid- 2,3(A)-D and oxaloacetic acid-3(A)-D, etc. When the two citric acids were treated with aconitate hydratase and isocitrate dehydrogenase, the deuterium from fumaric acid-2,3-D (VIII) appeared in NADPH, while the deuterium from D20 did not. The hydrogen which exchanges with the hydrogen of the medium in the presence of aconitate hydratase is therefore attached to C-4 in the posterior position (see II and XVI). The stereochemistry of the aconitate hydratase reaction follows: The addition of T20 to cis-aconitate (XVII) to give citrate-4(P)-T (XVI) or to give threo-D§-isocitrate-3-T (XVIII) is trans in both cases. A given double-bond carbon atom is always attacked from the same side. Gawron et al.33 have already noted that these conclusions follow if C-1 and C-2 of citrate are acetate-derived. The stereochemistry of the 5-dehydroquinate dehydratase reaction may also be inferred. Thus, if the enzymatic hydration of 5-dehydroshikimate (III) is cis, then citric acid-4(P)-T (XX) is obtained via the intermediates 5-dehydroquinic

T OH HO, COOH HO, COOH HI, V-COOH H COOH H-, sCOOH T\ T ~ C

C COON H 4C0, H. CHC COOH / \COO HOOC COOH I OHCOH H,~~~IC COCOON 0 O HOOC XVI HOOC XVII HOOC XVIII OH XIX XX FIG. 4. FIG. 5. Downloaded by guest on September 30, 2021 VOL. 50, 1963 BIOCHEMISTRY: HANSON AND ROSE 987

- H acid-6(P)-T (XIX) and quinic acid-6(A)-T. OH OH C - - C C This appears to be the first example of en- 0 IOH 0 -oc-c=c -c - ooc- c J -c- zymatic cis addition to a double bond. HXH"OIHOH H In considering the mechanism of the 5- OH, H' L OOC--C = - - OH HI dehydroquinate dehydratase reaction, it first be noted that the of FIG. 6. may position OH FIG.6. attack on 5-dehydroshikimate (III) is j3 to the C-5 keto group. Such an addition is in accordance with experience for nonenzymatic reactions: the keto group shows a stronger directing influence than the carboxyl ion. The addition process need not be formulated as a concerted addition to the double bond. By analogy with the behavior of unconjugated double bonds, an addition of this type might be expected to be trans. If the addition to the a and f3 positions takes place in two separate stages, then the stereochemistry will depend entirely upon the arrangement of acceptor-donor groups on the enzyme. Examples of such two stage mechanisms are shown in Figure 6. The nucleo- phylic addition of methoxy to trans-dibenzoylethylene has been formulated in terms analogous to the first mechanism. The methoxyl addition is here the rate- determining step.35 Summary of Conclusions.-(1) If a molecule of biosynthetically formed citric acid is viewed from the side opposite the middle COOH group, then moving from OH in a counterclockwise direction the first -CH2COOH is derived from acetyl- CoA, and the second from oxaloacetate. (2) The enzymatic addition of water to cis-aconitate to give citrate is trans. (3) The enzymatic addition of water to 5-dehydroshikimate to give 5-dehydroquinate is cis. Nomenclature: The Hirschmann rules"' for designating the various atoms about a meso carbon atom have been used in this paper wherever appropriate. The various compounds in which tritium or deuterium has replaced protium, however, are asymmetric in the conventional sense and the configurations at the asymmetric centers may be fully specified by the RIS system.36 Since the A/P system is linked to the RIS system, and since protium has the lowest priority of any substituent, replacement of protium in the P position by deuterium or tritium necessarily gives R asymmetry, and replacement in the A position gives S asymmetry. It follows that citric acid-4(P)-T is (2R,3R)-2-tritiocitric acid (sub-rules 1 and 4) and quinic acid-6(A)-T is (6S)-e-tritioquinic acid or (lR,2S,3R,4S,5R)-1,3,4,5-trihydroxy-2-tritiocyclohexane-1-carboxylic acid (sub-rules 1 and 4). Quinic acid itself is (1R,3R,4S,5R)-1,3,4,5-trihydroxycyclohexane-1-carboxylic acid (C-3 and C-5 by sub-rule 1, C-1 and C-4-by sub-rule 2). (We are indebted to Dr. Cahn for his comments on the application of the RIS system to the quinic acids.) Threo-D8-isocitric acid is (2R,3S)-isocitric acid and tritium substitution does not alter the RIS labels. The fluorocitric acid derived biosynthetically from fluoroacetate is either (2S,3S)- or (2R,3S)-2-fluorocitric acid.3) The asymmetric centers of citric acid-4(P)-T may also be defined by extending carbohydrate- amino acid nomenclature in the manner used for the isocitric acids.3" The procedure leads to the names D.D,-2-tritiocitric acid or erythro-D.-2-tritiocitric acid (the COOH attached to C-3 is here disregarded).

* Support of part of this work by the National Science Foundation and the U.S. Public Health Service (A-4517) is gratefully acknowledged. t Present address: Institute for Cancer Research, Philadelphia, 11, Pennsylvania. I Ogston, A. G., Nature, 162, 963 (1948). 2 Potter, V. R., and C. Heidelberger, Nature, 164, 180 (1949). 3 Wilcox, P. E., C. Heidelberger, and V. R. Potter, J. Am. Chem. Soc., 72, 5019 (1950). 4Lorber, V., M. F. Utter, H, Rudney, and M. COQok, J. Biol. Chem., 185, 689 (1950). Downloaded by guest on September 30, 2021 988 MATHEMATICS: WEISS AND ZELEN PROC. N. A. S.

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A STOCHASTIC MODEL FOR THE INTERPRETATION OF CLINICAL TRIALS* BY GEORGE H. WEISSt AND MARVIN ZELENI UNIVERSITY OF MARYLAND AND MATHEMATICS RESEARCH CENTER, U.S. ARMY Communicated by J. Neyman, September 12, 1963 1. Introduction.-There are several diseases in which possibly recurrent phases may be distinguished. Different investigators have proposed Markovian models to describe data dealing with the time-dependent phenomena associated with these diseases. We mention in particular the work of Fix and Neyman on cancer,' the Downloaded by guest on September 30, 2021